Combine all ingredients except for beef, fillings, and sauce ingredients to make marinade. If it seems a little dry, add a little olive oil (a tablespoon at a time). Here is an excellent tahini recipe, if you do not have some handy.
Add beef, cover and refrigerate at least 8 hours, preferably overnight.
In a stockpot or large saucepan, cook beef over medium heat for 45 minutes or until done. Be sure not to overcook!
If beef becomes a little dry, add a few tablespoons of water throughout cooking duration.
While beef is cooking, prepare the sauce. Combine sauce ingredients and mix well. Set aside.
Take the onions, tomatoes, cucumbers and sprinkle with sumac. Add other filling ingredients in a large bowl and combine well.
When the beef is done, you can shred it, slice it, or leave into large pieces. As long as it it thinly cut, there is not much difference. I prefer to cut mine into wide strips.
Prepare the Pita
Place enough beef on pita that cover 1/4 of the loaf. Add veggies and pour sauce. Roll like a soft taco or burrito and you have shawarma! You can also stuff the pocket of the pita if you like. I prefer to roll large pitas (this is where making your own pita comes in handy), but it is hard to find large loaves of pita at the supermarket.
You can serve shawarma with fries, falafel, hummus, or with a salad like tabouleh.